ONLY ONE OPTION IS CORRECT. Take approx. 2 minutes for answering each question.

Q.1

A wave is propag propagating ating along x-axis. x-axis. The displa displaceme cement nt of partic particles les of the medium medium in z-dire z-directio ction n at t = 0 is given by: z = exp[ –(x + 2) 2] , where ‘x’ is in meters. At t = 1s, the same wave disturbance distu rbance is given by: 2 z = exp[ – (2 – x) ]. Then, the wave propagation velocity velocity is (A) 4 m/s in + x direction (B) 4 m/s in –x direction (C) 2 m/s in + x direction (D) 2 m/s in – x direction

Q.2 Q. 2

The equation equation of a wave travelling travelling along the positive positive x-axis, as shown in figure at t = 0 is given by

kx t t kx (C) sin t kx (A) sin kx t (B) sin (D) sin 6 6 6 6 Q.3

Figure Figure shown shown the the shap shapee of part of a long string string in which which transverse waves are produced by attaching one end of the string to tuning fork of frequency 250 Hz. What is the velocity of the waves? (A) 1.0 ms –1 (B) 1.5 ms –1 (C) 2.0 ms –1 (D) 2.5 ms –1

Q.4

A block block of mass 1 kg is hanging hanging vertically vertically from from a string of length length 1 m and mass/length = 0.001 Kg/m. A small pulse is generated at its lower end. The pulse reaches the top end in approximately (A) 0.2 sec (B) 0.1 sec (C) 0.02 sec (D) 0.01 sec

Q.5

A uniform rope rope having having some some mass hanges vertically from a rigid support. A transverse wave pulse pulse is produ produced ced at the lower lower end. end. The The spee speed d (v) (v) of the wave wave pul pulse se varies varies with with hei heigh ghtt (h) (h) from from the lower lower end end as: as:

(A)

Q.6

(C)

(D)

A wire ire of 10 –2 kgm kgm –1 passes over a frictionless light pulley fixed on the top of a frictionless inclined plane which makes an angle of 30° with the horizontal. Masses m and M are tied at two ends of wire such that m rests on the plane and M hangs freely vertically downwards. The entire system is in equilibrium and a transverse wave propagates along the wire with a velocity of 100 ms –1. (A) M = 5 kg

Q.7

(B)

(B)

m M

=

1 4

(C) m = 20 kg

(D)

m M

= 4

A pulse shown here is reflected reflected from the rigid wall A and then from free end B. The shape of the string after these 2 reflection will be (A)

(B)

(C)

(D)

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Q.8 Q. 8

A composition composition string is made made up by joining two strings strings of different masses per unit length and 4. The composite string is under the same tension. A transverse wave pulse : Y = (6 mm) sin(5t + 40x), where ‘t’ is in seconds and ‘x’ in meters, is sent along the lighter string towards the joint. The joint is at x = 0. The equation of the wave pulse reflected from the joint is (A) (2 mm) sin(5t – 40x) (B) (4 mm) sin(40x – 5t) (C) – (2 mm) sin(5t – 40x) (D) (2 mm) sin (5t – 10x)

Q.9

In the previous question, question, the percentage percentage of power power transmitted transmitted to the the heavier heavier string through the joint joint is approximately (A) 33% (B) 89% (C) 67% (D) 75%

Q.10

A wave pulse on a string has has the dimension shown in figure. The waves waves speed is v = 1 cm/s. If point O is a free end. The shape of wave at time t = 3 s is :

(A)

(B)

(C)

(D)

Q.11 Q. 11

A string 1m long is drawn by a 300Hz vibrator vibrator attached attached to its end. The string vibrates vibrates in 3 segments. The speed of transverse waves in the string is equal to (A) 100 m /s (B) 200 m/ s (C ) 300 m /s (D) 400 m/ s

Q.12

A wave is represent represented ed by the equation equation y = 10 sin sin 2 (100t0.02x) + 10 sin 2 (100t+0.02x). The maximum amplitude and loop length are respectively (A) 20 units and 30 units (B) 20 units and 25 units (C) 30 units and 20 units (D) 25 units and 20 units

Q.13 Q.13

The resultant resultant amplitude amplitude due to superposition superposition of two waves y 1 = 5sin (wt y2 = 5 cos (wt kx 150°) (A) 5

(B) 5 3

(C) 5 2 3

kx) and

(D) 5 2 3

Q.14

A wave represented represented by the equation equation y = A cos (kx – t) is superimposed with another wave to form a statioary wave such that the point x =0 is a node. The equation of the other wave is: (A) –A sin (kx + t) (B) (B) – A cos cos (kx (kx + t) (C) A sin (kx + t) (D) A cos (kx + t)

Q.15

A taut string string at at both both ends vibrates vibrates in its its n th overtone. The distance between adjacent Node and Antinode is found to be 'd'. If the length of the string is L, then (A) L = 2d (n + 1) (B) L = d (n + 1) (C) L = 2dn (D) L = 2d (n – 1)

Q.16 Q. 16

A metallic wire of length L is fixed between two rigid supports. If If the wire is cooled cooled through through a temperature difference T (Y = young’s modulus, = density, = coefficient of linear expansion) then the frequency of transverse vibration is proportional to : (A)

Q.17

Y

(B)

A standing wave y = A sin

Y

(C)

Y

(D)

Y

20 x cos (1000t) is maintained in a taut string where y and x are 3

expressed in meters. meters. The distance between the successive points points oscillating with the amplitude amplitude A/2 across a node is equal to (A) 2.5cm (B) 25cm (C) 5cm (D) 10cm

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Q.18

A string string of length 1m and and linear linear mass density density 0.01kgm 0.01kgm 1 is stretched to a tension of 100N. When both ends of the string are fixed, the three lowest frequencies for standing wave are f 1, f 2 and f 3. When only one end of the string is fixed, the three lowest frequencies for standing wave are n 1, n2 and n3. Then (A) n3 = 5n1 = f 3 = 125 Hz (B) f3 = 5f 1 = n2 = 125 Hz (C) f 3 = n2 = 3f 1 = 150 Hz

Q.19

Q.20 Q.2 0

4

(B)

3

16

(C)

9

uvt

uv

(D)

12

32 27

(B)

t ( u v) uv

(C)

t ( u v) uv

(D)

uvt uv

A wave travels travels uniformly uniformly in all directions directions from from a point source source in an isotropic isotropic medium. medium. The displace displacement ment of the medium at any point at a distance r from the source may be represented by (A is a constant representing strength of source) (A) [A/

r ] sin (kr – t)

(B) [A/r] sin (kr – t)

(C) [Ar] sin (kr – t) Q.22

15

A firecracke firecrackerr exploding exploding on the surface surface of of a lake is heard as two sounds sounds a time interval interval t apart apart by a man on a boat close to water surface. Sound travels with a speed u in water and a speed v in air. The distance from the exploding firecracker to the boat is (A)

Q.21 Q.2 1

f 1 f 2

= 75 Hz 2 The frequency frequency of a sonometer sonometer wire is f, but when the weights producing producing the tensions are completely immersed in water the frequency becomes f/2 and on immersing the weights in a certain liquid the frequency becomes f/3. The specific gravity of the liquid is: (A)

(D) n2 =

(D) [A/r2] sin (kr – t)

How many many times more more intense intense is 90 dB sound than 40 dB sound? (A) 5 (B) 50 (C) 500

(D) 10 5

Q.23 Q.2 3

Three coherent coherent waves waves of equal frequencies frequencies having amplitude 10 m, 4m and 7 m respectively, arrive at a given point with successive phase difference of /2. The amplitude of the resulting wave in mm is given by (A) 5 (B) 6 (C) 3 (D) 4

Q.24 Q.2 4

A person person standing standing at at a distance distance of 6 m from a source of sound sound receives receives sound sound wave wave in two ways, one directly from the source and other after reflection from a rigid bounda boundary ry as shown shown in in the the figure figure.. The The maximu maximum m wave wavelen length gth for for whic which, h, the the perso person n will receive maximum sound intensity, is (A) 4 m

(B)

16 3

m

(C) 2 m

(D)

8 3

m

Q.25

The ratio of intensities intensities between between two two coherent coherent soud sources sources is 4 : 1. The differen differenmce mce of loudnes loudnesss in dB betw betwee een n maxi maximu mum m and and minimu minimum m int inten ensi siti ties es when when they they inte interf rfer eree in spac spacee is: is: (A) 10 log 2 (B) 20 log 3 (C) 10 log 3 (D) 20 log 2

Q.26

In Quincke’ Quincke’ss tube a detector detector detects detects minimum intensity intensity.. Now one of the tube tube is displaced displaced by 5 cm. cm. During displacement detector detects maximum intensity 10 times, then finally a minimum intensity (when displacement is complete). The wavelength of sound is: (A) 10/9 cm (B) 1 cm (C) 1/2 cm (D) 5/9 cm

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Q.27 Q.2 7

The ratio ratio of maximum to minimum intensity intensity due to superpositio superposition n of two waves waves is

49 9

. Then the ratio of

the intensity of component waves is (A)

25 4

(B)

16 25

(C)

4

(D)

49

9 49

Q.28

Two waves of of sound having intensities I and 4I interfere to produce interference interference pattern. The phase difference between the waves is /2 at point A and at point B. Then the difference between the resultant intensities at A and B is (A) 2I (B) 4I (C) 5I (D) 7I

Q.29 Q. 29

Sound waves of frequency frequency 660 Hz fall normally on a perfectly reflecting wall. The shortest distance from the wall at which the air particle has maximum amplitude of vibration is (velocity of sound in air is 330 m/s) (A) 0.125 m (B) 0.5 m (C) 0.25 m (D) 2 m

Q.30 Q.3 0

An open organ pipe of length L vibrates vibrates in second harmonic mode. The pressure vibration is maximum (A) at the two ends (B) at a distance L/4 from either end inside the tube (C) at the mid-point of the tube (D) none of these

Q.31 A n open is sounded together with another organ pipe of length l + + x in their open organ organ pipe of l ength l is fundamental tones (x << l ). ). The beat frequency heard will be (speed of sound is v) : (A)

vx 4l 2

(B)

vl 2 2x

vx

(C)

2 l 2

(D)

vx2 2 l

Q.32

A sufficie sufficiently ntly long long close organ organ pipe has has a small hole at its bottom. bottom. Initially the pipe is empty. empty. W Water ater is poured poured into into the the pipe pipe at a consta constant nt rate rate.. The fundam fundament ental al freq frequen uency cy of the the air column column in the the pipe pipe (A) continuously increasing (B) firs firstt inc increas reasees and the them becom ecomees cons consta tant nt (C) con continu tinuou ousl sly y decrea reases ses (D) (D) firs firstt dec decreas reases es and and the them beco become me cons consta tant nt

Q.33

A tuning tuning fork fork of frequency frequency 340 340 Hz is vibrated vibrated just above a cylindrical cylindrical tube of length 120 120 cm. Water Water is –1 slowly poured in the tube. If the speed of sound is 340 ms then the minimum height of water required for resonance is: (A) 95 cm (B) 75 cm (C) 45 cm (D) 25 cm

Q.34

An orga organ n pipe pipe P1 closed at one end vibrating in its first overtone. Another pipe P 2 open at both ends is vibrating in its third overtone. They are in a resonance with a given tuning fork. The ratio of the length of P1 to that of P2 is : (A) 8/3 (B) 3/8 (C) 1/2 (D) 1/3

Q.35

In a closed end end pipe of length 105 cm, standing standing waves waves are set up corresponding corresponding to the third third overtone. overtone. What distance from the closed end, amongst the following, is a pressure Node? (A) 20 cm (B) 60 cm (C) 85 cm (D) 45 cm

Q.36 Q.3 6

A pipe’s pipe’s lower end is immersed in water such that the length of air column from the top open end has a certain length 25 cm. The speed of sound in air is 350 m/s. The air column is found to resonate with a tuning fork of frequency 1750 Hz. By what minimum distance should the pipe be raised in order to make the air column resonate again with the same tuning fork? (A) 7 cm (B) 5 cm (C) 35 cm (D) 10 cm

Q.37

In case of closed organ pipe which harmonic harmonic the the p th overtone will be (A) 2p + 1 (B) 2p 1 (C) p + 1

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(D) p 1

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Q.38

A closed closed organ organ pipe of radius radius r 1 and an open organ pipe of radius r 2 and having same length 'L' resonate when excited with a given tunning fork. Closed organ pipe resonates in its fundamental mode where as open organ pipe resonates in its first overtone, then (A) r 2 – r 1 = L (B) r2 – r 1 = L/2 (C) r2 – 2r 1 = 2.5 L (D) 2r 2 – r 1 = 2.5 L

Q.39 Q.3 9

First overtone overtone frequency frequency of a closed closed organ pipe is equal equal to the first overtone overtone frequency frequency of an open open organ organ pipe. pipe. Furthe Furtherr nth nth harmon harmonic ic of closed closed organ organ pipe pipe is is also also equal equal to the the mth harmon harmonic ic of open open pipe, pipe, where where n and m are: (A) 5, 4 (B) 7, 5 (C) 9, 6 (D) 7, 3

Q.40 .40

If l1 and l2 are the lengths of air column for the first and second resonance when a tuning fork of frequency n is sounded on a resonance tube, then the distance of the displacement antinode from the top end of the resonance tube is: (A) 2(l2 – l1)

(B)

1 2

(2l1 – l2)

(C)

l 2 3l1 2

(D)

l 2 l1 2

Q.41

A closed closed orgain orgain pipe has length length ‘ l ’. ’. The air in it is vibrating in 3 rd overtone with maximum displacement amplitude ‘a’. The displacement amplitude at distance l / 7 from closed end of the pipe is: (A) 0 (B) a (C) a / 2 (D) none of these

Q.42 Q.4 2

The first resonance length of of a resonance resonance tube is 40 cm and the second resonance length is 122 cm. The The third resonance length of the tube will be (A) 200 cm (B) 202 cm (C) 203 cm (D) 204 cm

Q.43 Q.4 3

A tuning fork of frequency frequency 280 280 Hz produces produces 10 beats per sec when when sounded with a vibrating vibrating sonometer string. When the tension in the string increases slightly, it produces 11 beats per sec. The original frequency of the vibrating sonometer string is : (A) 269 Hz (B) 291 Hz (C) 270 Hz (D) 290 Hz

Q.44 Q.4 4

Two tuning forks forks A & B produce notes of frequencies frequencies 256 256 Hz & 262 Hz respective respectively ly.. An unknown note note sounded at the same time as A produces beats . When the same note is sounded with B, beat frequency is twice as large . The unknown frequency could be : (A) 268 Hz (B) 260 Hz (C) 250 Hz (D) 242 Hz

Q.45 Q.4 5

A closed organ pipe and an open pipe of same length produce 4 beats when they are set into vibrations simultaneously. simultaneously. If the length of each of them were twice their initial lengths, the number of beats produced will be (A) 2 (B) 4 (C) 1 (D) 8

Q.46

The speed speed of sound sound in a gas, in in which two waves of of wavelength wavelength 1.0 m and 1.02 1.02 m produce produce 6 beats beats per second, is approximately: (A) 350 m/s (B) 300 m/s (C) 380 m/s (D) 410 m/s

Q.47 Q.4 7

In a test of subsonic subsonic Jet flies over head at an altitude of 100 m. The sound intensity on the ground as the Jet passes overhead is 160 dB. At what altitude should the plane fly so that the ground noise is not greater than 120 dB. (A) above 10 km from ground (B) above 1 km from ground (C) above 5 km from ground (D) above 8 km from ground

Q.48

The frequency frequency changes changes by by 10% as as a sound source source approaches approaches a stationary stationary observer observer with constant constant speed vs. What would be the percentage change in frequency as the source recedes the observer with the same speed. Given that v s < v. (v = speed of sound in air) (A) 14.3% (B) 20% (C) 10.0% (D) 8.5%

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Q.49

Consider Consider two sound sound sources sources S 1 and S2 having same frequency 100Hz and the observer O located between them as shown in the fig. All the three are moving with same velocity in same direction. The beat frequency of the observer is (A) 50Hz (B) 5 Hz (C) zero (D) 2.5 Hz

Q.50 Q.5 0

An engine engine whistling whistling at a constant constant frequency frequency n 0 and moving with a constant velocity goes past a stationary observer. As the engine crosses him, the frequency of the sound heard by him changes by a factor f. The actual difference in the frequencies of the sound heard by him before and after the engine crosses him is (A)

Q.51 Q.5 1

1 2

1 f 2 (B) n0 f 2 1

n0(1 f ) 2

(C) n0

1 f 1 f

(D)

1 2

n0

1 f 1 f

Source and observer observer both start start moving simultaneously simultaneously from origin, origin, one along x-axis x-axis and the the other other along y-axis with speed of source = twice the speed of observer. The graph between the apparent frequency observed by observer f and time t would approximately be :

(A)

(B)

(C)

(D)

Q.52

A stationary sound source source 's' of frequenc frequency y 334 Hz and a stationary observer observer 'O' are placed placed near a reflecting surface moving away from the source with velocity 2 m/sec as shown in the figure. If the velocity of the sound waves is air is V = 330 m/sec, the apparent frequency of the echo is (A) 332 Hz (B) 326 Hz (C) 334 Hz (D) 330 Hz

Q.53

A source source S of of freq frequen uency cy f 0 and an observer O, moving with speeds v 1 and v2 respectively, are movinng away from each other. When they are separated by distance a (t =0), a pulse is emitted by the source. This pulse is received by O at time t 1 then t1, is equal to (A)

a v s v2

(B)

a v1 vs

a

(C) v v s 2

(D)

a v1 v 2 vs

Q.54

A detector detector is released released from rest over over a source of sound sound of frequency frequency 3 f 0 = 10 Hz. The frequency observed by the detector at time t is plotted in the graph. The speed of sound in air is (g = 10 m/s 2) (A) 330 m/s (B) 350 m/s (C) 300 m/s (D) 310 m/s

Q.55 Q.5 5

An observer observer starts moving with uniform uniform acceleration acceleration 'a' towards towards a stationary stationary sound source source of frequency frequency f. As the observer approaches the source, the apparent frequency f' heard by the observer varies with time t as:

(A)

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(B)

(C)

(D)

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Q.56

A sounding body of negligible dimension emitting a frequency of 150 Hz is dropped from a height. height. During its fall under gravity it passes near a balloon moving up with a constant velocity of 2m/s one second after it started to fall.The difference in the frequency observed by the man in balloon just before and just after crossing the body will be : (Given that -velocity of sound = 300m/s; g = 10m/s 2) (A) 12 (B) 6 (C) 8 (D) 4

Q.57 Q.5 7

A source of of sound S having frequency frequency f. Wind Wind is blowing from source to observer O with velocity u. If speed of sound with respect to air is C, the wavelength of sound detected by O is: (A)

Cu

(B)

f

Cu f

(C)

CC u

C u f

(D)

C f

ONE OR MORE THAN ONE OPTION MAY BE CORRECT Take approx. 3 minutes for answering each question.

Q.1 Q. 1

A sinusoidal progressive wave is generated in a string. It’s It’s equation is given given by y = (2 mm) sin (2 x – 100 t + /3). The time when particle at x = 4 m first passes through mean posi positi tion on,, wil willl be be (A)

1 150

sec

(B)

1 12

sec

(C)

1 300

sec

(D)

1 100

sec

Q.2

A transve transverse rse wave is descr described ibed by the equation equation y = A sin [2 [2 (f t – x/) ].The maximum particle velocity is equal to four times the wave velocity if: (A) = A/4 (B) = A/2 (C) = A (D) = 2A

Q.3

A wave equation is given given as as y = cos(500t cos(500t – 70x), where y is in mm, x in m adn t is in sec. sec. (A) the wave must be a transverse porpagating wave. (B) The speed of the wave is 50/7 m/s (C) The frequency of oscillations 1000 Hz (D) Two closest points which are in same phase have separation 20 /7 cm.

Q.4

At a certain certain moment, moment, the the photo photogra graph ph of a string string on which which a harmonic harmonic wave is travelling to the right is shown. Then, which of the following is true regarding the velocities of the points P, Q and R on the string. (A) vP is upwards (B) vQ = – vR (C) | vP | > | vQ | = | v R | (D) vQ = vR

Question No. 5 to 8 (4 questions) The figure represents the instantaneous picture of a transverse harmonic wave traveling along the negative x-axis. Choose the correct alternative(s) related to the the movement of the nine points shown in the figure.

Q.5 Q.6 Q.7

The point pointss moving moving upwar upward d is/ar is/aree (A) a (B) c

(C) f

(D) g

The points points moving moving downward downwardss is/are is/are (A) o (B) b

(C) d

(D) h

The statio stationar nary y points points is/are is/are (A) o (B) b

(C) f

(D) h

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Q.8 Q. 8

The points points moving moving with maximum maximum velocity velocity is/are is/are (A) b (B) c (C) d

(D) h

Q.9

A perfectly perfectly elastic elastic uniform uniform string string is suspende suspended d vertica vertically lly with with its upper end fixed fixed to the ceiling ceiling and the the lower end loaded with the weight. If a transverse wave is imparted to the lower end of the string, the puls pulsee will will (A) not travel travel along along the length length of the string string (B) travel travel upwards upwards with increasing increasing speed speed (C) travel upwards upwards with decreasing decreasing speed (D) travelled travelled upwards upwards with constant constant accelera acceleration tion

Q.10 Q.1 0

One end of a string of length length L is tied tied to the ceiling ceiling of a lift accelerat accelerating ing upwards upwards with an an acceleration acceleration 2g. 2g. The other end of the string is free. The linear mass density of the string varies linearly from 0 to from bottom to top. top. (A) The velocity of the wave in the string will be 0. (B ) The ) The acceleration of the wave on the string will be 3g/4 every where. (C ) The ) The time taken by a pulse to reach from bottom to top will be

8L / 3g .

(D) The time taken by a pulse to reach from bottom to top will be

4L / 3g .

A plane plane wave wave y=A y=A sin t

x

Q.11

undergo a normal incidence on a plane boundary separating separating medium v M1 and M2 and splits into a reflected and transmitted wave having speeds v 1 and v2 then (A) for all values of v 1 and v2 the phase of transmitted wave is same as that of incident wave (B) for all values of v 1 and v2 the phase of reflected wave is same as that of incident wave (C) the phase of transmitted wave depends upon v 1 and v2 (D) the phase of reflected wave depends upon v 1 and v2

Q.12 Q.1 2

The vibration vibration of a string string fixed at both ends are are described described by Y= 2 sin( sin( x) sin(100t) where Y is in mm,x is in cm,t in sec then (A)Maximum displacement of the particle at x = 1/6 cm would be 1 mm. (B) velocity of the particle at x = 1/6 cm at time t = 1/600 sec will be 157 3 mm/s (C) If the length of the string be 10 cm, number of loop in it would be 5 (D) None of these

Q.13

In a standing standing wave on a string. string. (A) In one time period all the particles are simultaneously at rest twice. (B) All the particles must be at their positive extremes simultaneously once once in one time period. (C) All the particles may be at their positive extremes simultaneouslyonce simultaneouslyonce in a time period. (D) All the particles are never at rest simultaneously.

Q.14 Q.1 4

A standing standing wave wave pattern of of amplitude A in a string of length L shows 2 nodes nodes (plus those at at two ends). If If one end of the string corresponds to the origin and v is the speed of progressive wave, the disturbance in the string, could be represented (with appropriate phase) as:

2x cos 2vt L L

(B) y( x , t ) A cos

4x cos 4vt L L

(D) y( x , t ) A sin

(A) y( x , t ) A sin

(C) y( x, t ) A cos

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3x sin 3vt L L

3x cos 3vt L L

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[11]

Q.15

The length, length, tension, tension, diameter diameter and density density of of a wire B are are double than than the corresp corresponding onding quantitie quantitiess for another stretched wire A. Then. (A) Fundamental frequency of B is (B) The velocity of wave in B is

1 2

1 2 2

times that of A.

times that of velocity in A.

(C) The fundamental frequency of A is equal to the third overtone of B. (D) The velocity of wave in B is half that of velocity in A. Q.16 Q. 16

A string is fixed at at both ends ends vibrates vibrates in a resonant mode with a separation 2.0 cm between between the consecutive consecutive nodes. For the next higher resonant frequency, this separation is reduced to 1.6 cm. The length of the string is (A) 4.0 cm (B) 8.0 cm (C) 12.0 cm (D) 16.0 cm

Q.17 Q.1 7

A clamped clamped string is oscilla oscillating ting in nth harmonic, harmonic, then (A ) total ene energy rgy of oscil oscillations lations wi ll be n2 times that of fundamental frequency (B) total energy of oscillations will be (n–1) 2 times that of fundamental frequency (C) average kinetic energy of the string over a complete oscillations is half of that of the total energy of the string. (D) none of these

Q.18

Figure, Figure, shows shows a stationary stationary wave between between two fixed fixed points points P and Q. Which point(s) point(s) of of 1, 2 and 3 are in phase phase with with the point X? (A) 1, 2 and 3 (B) 1 and 2 only (C) 2 and 3 only (D) 3 only

Q.19 Q.1 9

Which of the following following statements statements are wrong wrong about the the velocity velocity of sound sound in air: (A) decrea decreases ses with increases increases in tempera temperature ture (B) increases increases with decrease decrease in temper temperature ature (C) decr decrea ease sess as humid humidity ity incre increas ases es (D) (D) inde indepe pend nden entt of dens densit ity y of air air.

Q.20 Q.2 0

The particle particle displace displacement ment of a travelling travelling longitudional longitudional wave wave is represented represented by = (x, t). The midpoints of a compression zone and an adjacent rarefaction zone are represented by the letter ‘C’ and ‘R’. Which of the following is true? (A) | / x|C = | / x|R (B) | / t|C = | / t|R = 0 / x|C x Bulk modulus of air. (C) (pressure) C – (pressure)R = 2 | (D) Particles of air are stationary mid-way between ‘C’ and ‘R’.

Q.21 Q.22 Q.23

Question No. 21 to 26 (6 questions) The figure represents the instantaneous picture of a longitudinal harmonic wave travelling along the negative x-axis. Identify the correct statement(s) related to the movement of the points shown in the figure. The points points moving moving in the the direct direction ion of wave are (A) b (B) c (C) f (D) i

The points points moving moving opposite opposite to the directi direction on of of propagat propagation ion are are (A) a (B) d (C) f

(D) j

The stationary stationary points points are (A) a (B) c

(D) k

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(C) g

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Q.24 Q.25 Q.26 Q.2 6

Q.27

The maximum maximum displac displaced ed points points are (A) a (B) e

(C) g

(D) i

The points points of maximum maximum compress compression ion are (A) c (B) g

(C) e

(D) k

The points of maximum rarefaction rarefaction are (A) a (B) e

(C) g

(D) i

(C ) )

(D)

Which of the the following following graphs graphs is/are is/are corr correct. ect.

(A)

(B )

Q.28 Q.2 8

Two waves are are propagatin propagating g along a taut taut string that that coincides coincides with the x-axis. x-axis. The first first wave has has the wave function y1 = Acos [k(x – vt)] and the second has the wave function y = A cos [k(x + vt) + ]. (A) For constructive interference at at x = 0, = . (B) For constructive in interference terference at x = 0, = 3. (C) For destructive interference at x = 0, = . (D) For destructive interference at x = 0, = 2.

Q.29 Q.2 9

Two interfering waves have the same wavelength, frequency, frequency, and amplitude. They are traveling in the same direction but are 90° out of phase. Compared to the individual waves, the resultant wave will have the same. (A) amplitude and velocity but different wavelength (B) amplitude and wavelength but different velocity (C) wavelength and velocity but different amplitude (D) amplitude and frequency but different velocity

Q.30 Q. 30

Question No. 30 to 34 (5 questions) A narrow tube is bent in the form of a circle of radius R, as shown in the figure. Two small holes S and D are made in the tube at the positions right angle to each other. A source placed at S generated a wave of intensity I 0 which is equally divided into two parts : One part travels along the longer path, while the other travels along the shorter path. Both the part waves meet at the point D where a detector is placed If a maxima is formed formed at at the detector detector then, then, the magnitude magnitude of wavelength wavelength of the wave produced is given by

(A) R Q.31

R 2

(C)

R 4

(D)

2R 3

If the minima is formed formed at at the detector then, the magnitude of wavelength wavelength of the wave produced is given by (A) 2R

Q.32 Q.3 2

(B)

(B)

3R 2

(C)

2R

The maximum intensity produced produced at D is given by (A) 4I0 (B) 2I0 (C) I0

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3

(D)

2R 5

(D) 3I0

Objective Question Bank On Mechanical Waves

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Q.33

Q.34

Q.35

Q.36

The maximum maximum value value of to produce a maxima at D is given by (A) R

(B) 2R

(C)

(A) R

(B) 2R

(C)

R

2 The maximu maximum m value value of to produce a minima at D is given by

R

(D)

(D)

3R 2 3R

2 2 The second overtone of an open organ pipe pipe A and a closed closed pipe B have have the same frequency frequency at a given temperature. It follows that the ratio of the (A) length of A and B is 4 : 3 (B) fundamental frequencies of A & B is 5 : 6 (C) lengths of B to that of A is 5 : 6 (D) frequencies of first overtone of A & B is 10 : 9

Four open organ pipes of different different lengths lengths and different different gases gases at same temperature as shown in figure. Let f A, f B, f C and f D be their fundamental frequencies then :[Take

CO = 7/5] 2

(A) f A/f B = 2

(B) f B/f C = 72 28

(C) f C/f D = 11 28

(D) f D/f A = 76 11

Q.37

A gas is is filled in an organ organ pipe and and it is sounded sounded with with an organ organ pipe pipe in fundamental fundamental mode. Choose Choose the correct statement(s) : (T = constant) (A ) If I f gas gas is cha change nged d from f rom H 2 to O2, the resonant frequency will increase (B) If gas is changed from O 2 to N2, the resonant frequency will increase (C) If gas is changed from N 2 to He, the resonant frequency will decrease (D) If gas is changed from He to CH 4, the resonant frequency will decrease

Q.38 Q. 38

A closed organ pipe pipe of length length 1.2 m vibrates vibrates in its first overtone overtone mode. mode. The pressure pressure variation variation is maximum at: (A) 0.8 m from the open end (B) 0.4 m from the open end (C) at the open end (D) 1.0 m from the open end

Q.39

The equati equation on of a wave wave disturb disturbance ance is given given as as : y = 0.02 cos

50 t cos (10x), where x and y are 2

in meters and t in seconds. Choose the wrong statement: (A) (A) Anti Antino node de occu occurs rs at x = 0.3 0.3 m (B) The The wav wavelen eleng gth is 0.2 m (C) The speed speed of the constituent constituent waves is 4 m/s (D) Node occurs at x = 0.15 m Q.40

For a certain organ pipe three successive resonance frequencies frequencies are observed observed at at 425 Hz, 595 Hz and 765 Hz respectively. If the speed of sound in air is 340 m/s, then the length of the pipe is: (A) 2.0 m (B) 0.4 m (C) 1.0 m (D) 0.2 m

Q.41

In an organ pipe whose whose one one end is is at x = 0, the pressure pressure is expresse expressed d by p = p0cos 3x sin 300t where x is in meter and t in sec. The organ pipe can be 2 (A) closed at one end, open at another with length = 0.5m (B) open at both ends, length = 1m (C) closed at both ends, length = 2m 2 (D) closed at one end, open at another with length = m 3

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Objective Question Bank On Mechanical Waves

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Q.42 Q.4 2

Two whistles A and and B each have a frequency frequency of 500Hz. A is stationary stationary and B is moving towards towards the right (away from A) at a speed of 50 m/s. An observer is between the two whistles moving towards the right with a speed of 25 m/s. The velocity of sound in air is 350 m/s. Assume there is no wind. Then which of the following statements are true: (A) The apparent frequency of whistle B as heard by A is 444Hz approximately (B) The apparent frequency of of whistle B as heard by the observer is 469Hz approximately (C) The difference in the apparent frequencies of A and B as heard by the observer is 4.5 Hz. (D) The apparent frequencies of the whistles of each other as heard by A and Bare the same.

Q.43

A source of sound moves towards an observer (A) the frequency of the source is increased. (B) the velocity of sound in the medium is increased. (C) the wavelength of sound in the medium towards the observer is decreased. (D) the amplitude of vibration of the particles is increased.

Q.44

A car car moves towards towards a hill hill with speed speed vc. It blows a horn of frequency f which is heared by an observer following the car with speed v 0. The speed of sound in air is v. v (A) the wavelength of sound reaching the hill is f v vc (B) the wavelength of sound reaching the hill is f v vo f (C) the beat frequency observed by the observer is v v c 2 v ( v v ) f c o (D) the beat frequency observed by the observer is 2 2 v vc

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Objective Question Bank On Mechanical Waves

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ANSWER KEY ONLY ONE OPTION IS CORRECT.

Q. 1 Q. 8 Q.15 Q.22 Q.29 Q.36 Q.43 Q.50 Q.57

A C A D A D D B A

Q. 2 Q. 9 Q.16 Q.23 Q.30 Q.37 Q.44 Q.51

D B B A B A C B

Q.3 Q.10 Q.17 Q.24 Q.31 Q.38 Q.45 Q.52

A D C A C C A D

Q. 4 Q. 11 Q.18 Q.25 Q.32 Q.39 Q.46 Q.53

D B D B B C B C

Q. 5 Q.12 Q.19 Q.26 Q.33 Q.40 Q.47 Q.54

C B D B C C A C

Q. 6 Q.13 Q.20 Q.27 Q.34 Q.41 Q.48 Q.55

C A D A B B D A

Q. 7 Q.14 Q.21 Q.28 Q.35 Q.42 Q.49 Q.56

A B B B D D C A

ONE OR MORE THAN ONE OPTION MAY BE CORRECT

Q. 1 Q. 5 Q. 9 Q.13 Q.17 Q.21 Q.25 Q.29 Q.33 Q.37 Q.41

C A,D B,D A,C A,C B A,D C A B,D C

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Q.2 Q.6 Q.10 Q.14 Q.18 Q.22 Q.26 Q.30 Q.34 Q.38 Q.42

B C B,C D D C C A,B,C B B B,C

Q. 3 Q. 7 Q.11 Q. 1 5 Q. 1 9 Q. 2 3 Q. 2 7 Q. 3 1 Q. 3 5 Q. 3 9 Q. 4 3

A,B,D B,C A,D C,D A,B,C,D A B,C A,C,D C,D C C

Q. 4 Q. 8 Q.12 Q.16 Q.20 Q.24 Q.28 Q.32 Q.36 Q.40 Q.44

Objective Question Bank On Mechanical Waves

C,D C,D A,B B A,C,D A,B,D C B C C B,D

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